Classical gas turbine thermodynamic cycle has undergone no change over the last decades. The most important efficiency improvements have been obtained by reducing thermal losses and raising the overall pressure ratio and peak temperature. Pressure gain combustion (PGC) represents an increasingly interesting solution to break out current technological limits. Indeed cycle models show that a pressure raise across the combustion process would reduce fuel consumption, increasing efficiency. Providing an efficiency close to the corresponding detonative technological concepts, constant volume combustion (CVC) represents a viable solution that still needs to be studied. In this work, the CV2 (constant-volume combustion vessel) installed at the Pprime laboratory (France) is numerically investigated using the high-fidelity compressible large eddy simulation (LES) solver AVBP. All the successive phases of the CVC cycle, i.e., air intake, fuel injection, spark-ignited combustion, and exhaust, are considered in the LES. Intake and exhaust valves are properly represented by novel boundary conditions able to mimic the valves impact on the flow without the need to directly consider their presence and dynamics during the simulation, reducing the computational costs. The spark ignition is modeled as an energy deposition term added to the energy equation. The combustion phase is treated by the dynamic version of the thickened flame model (DTFLES) extended to deal with nonconstant pressure combustion. Time-resolved particle imaging velocimetry (PIV) and pressure measurement inside the chamber reveal that cold and reactive turbulent flow are well captured in all the phases, showing the reliability of the approach and the models used.